Calculation of $\pi$ to 100,000 decimals
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- by Daniel Shanks and John W. Wrench PDF
- Math. Comp. 16 (1962), 76-99 Request permission
References
- George W. Reitwiesner, An ENIAC determination of $\pi$ and $e$ to more than 2000 decimal places, Math. Tables Aids Comput. 4 (1950), 11–15. MR 37597, DOI 10.1090/S0025-5718-1950-0037597-6
- S. C. Nicholson and J. Jeenel, Some comments on a NORC computation of $\pi$, Math. Tables Aids Comput. 9 (1955), 162–164. MR 75672, DOI 10.1090/S0025-5718-1955-0075672-5 G. E. Felton, “Electronic computers and mathematicians,” Abbreviated Proceedings of the Oxford Mathematical Conference for Schoolteachers and Industrialists at Trinity College, Oxford, April 8-18, 1957, p. 12-17, footnote p. 12-53. This published result is correct to only 7480D, as was established by Felton in a second calculation, using formula (5), completed in 1958 but apparently unpublished. For a detailed account of calculations of $\pi$ see J. W. Wrench, Jr., “The evolution of extended decimal approximations to $\pi$,” The Mathematics Teacher, v. 53, 1960, p. 644-650.
- François Genuys, Dix mille décimales de $\pi$, Chiffres 1 (1958), 17–22 (French). MR 94928 This unpublished value of $\pi$ to 16167D was computed on an IBM 704 system at the Commissariat à l’Energie Atomique in Paris, by means of the program of Genuys. C. Störmer, “Sur l’application de la théorie des nombres entiers complexes à la solution en nombres rationnels, ${x_1},\,{x_2},\, \cdot \cdot \cdot ,{x_n}$, ${c_1},\,{c_2},\, \cdot \cdot \cdot ,\,{c_n}$, k de l’équation ${c_1}$ $\operatorname {arctg}\,{x_1}\, + \,{c_2}$ $\operatorname {arctg}\,{x_2}\, + \, \cdot \cdot \cdot + \,{c_n}$ $\operatorname {arctg}\,{x_n}\, = \,{k\pi }/{4}$,” Archiv for Mathematik og Naturvidenskab, v. 19, 1896, p. 69. C. F. Gauss, Werke, Göttingen, 1863; 2nd ed., 1876, v. 2, p. 499-502.
- S. Ramanujan, Modular equations and approximations to $\pi$ [Quart. J. Math. 45 (1914), 350–372], Collected papers of Srinivasa Ramanujan, AMS Chelsea Publ., Providence, RI, 2000, pp. 23–39. MR 2280849, DOI 10.1016/s0164-1212(00)00033-9
Additional Information
- © Copyright 1962 American Mathematical Society
- Journal: Math. Comp. 16 (1962), 76-99
- MSC: Primary 65.99
- DOI: https://doi.org/10.1090/S0025-5718-1962-0136051-9
- MathSciNet review: 0136051